Lattice Boltzmann Model Using Two Relaxation Times for Shallow-Water Equations

Abstract

A lattice Boltzmann method with two relaxation times for shallow-water equations (LABSWETRT) without turbulence is proposed. The described model is validated through simulations of three typical cases with laminar flows: 1D steady flow over a bump, 2D unsteady dam-break flow, and flow around circular cylinder. Good agreement between prediction and analytical or experimental solutions are obtained. In addition, the performance of the LABSWETRT and the lattice Boltzmann method for shallow-water equations using a single relaxation time (LABSWE) is compared in detail. Studies have shown that the former is more stable than the latter for 2D cases. Different combinations of the two relaxation times are also studied and the optimized one is recommended for good numerical stability. This study demonstrates that the additional relaxation time in the LABSWETRT can improve the stability of simulations for laminar shallow flows using a procedure almost as simple as that in the LABSWE.